What is simplify-ln(10000)+3ln(5000-300) ?

The solution to simplify-ln(10000)+3ln(5000-300) is ln(10382300)

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simplify-ln(10000)+3ln(5000-300)

simplify

- ln (10000) + 3 ln (5000 - 300)

ln (10382300)

Decimal Notation

16.15561 \dots

Solution steps

- ln (10000) + 3 ln (5000 - 300)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (5000 - 300) = ln ((5000 - 300)^{3})

= - ln (10000) + ln ((5000 - 300)^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ((5000 - 300)^{3}) - ln (10000) = ln (\frac{( 5000 - 300 ) ^{3}}{10000})

= ln (\frac{( 5000 - 300 ) ^{3}}{10000})

\frac{( 5000 - 300 ) ^{3}}{10000} = 10382300

= ln (10382300)

ln (\frac{x ^{7}}{x ^{2} - 25})

- ln (\frac{x + 1}{x})

- lo g_{10} (5.3 \cdot 1 0^{- 5})

- lo g_{10} (3.4 \cdot 1 0^{- 11})

ln (9.5 \cdot 1 0^{- 6})

What is simplify-ln(10000)+3ln(5000-300) ?
The solution to simplify-ln(10000)+3ln(5000-300) is ln(10382300)